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Triangle and Point

  • Chapter
Recent Advances in Geometric Inequalities

Part of the book series: Mathematics and Its Applications ((MAEE,volume 28))

Abstract

Let P be a point in the plane of a triangle ABC, and let M be an arbitrary point in space. Then \( \overrightarrow {MP} = (\sum {{x_1}} \overrightarrow {MA} )/(\sum {{x_1}} ) \), where x1, x2, x3 are real numbers, and the following generalization of the well-known Leibniz identity is valid

$$ {(\sum {{x_1}} )^2}M{P^2} = \sum {{x_1}} \sum {{x_1}} M{A^2} - \sum {{a^2}{x_2}} {x_3}. $$
(1)

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  1. University of Belgrade, Yugoslavia

    D. S. Mitrinović

  2. University of Zagreb, Yugoslavia

    J. E. Pečarić & V. Volenec

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  1. D. S. Mitrinović
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Mitrinović, D.S., Pečarić, J.E., Volenec, V. (1989). Triangle and Point. In: Recent Advances in Geometric Inequalities. Mathematics and Its Applications, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7842-4_11

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